2024/04/09 by Yi Wang, Wang, Yi · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #Composite material #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Knot (papermaking) #Materials science #Mathematics #Pure mathematics #Torus
paper · pdf · doi:10.48550/arxiv.2404.06388
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/04/09 · openalex created_date 2024/04/12 · openalex updated_date 2026/07/28
The limiting character, introduced by Tillmann, has been studied recently in the context of Culler-Shalen theory. We extend the methods of the author's previous work to show that certain families of essential twice-punctured tori are detected by an ideal point on the character variety and determine the limiting character at these ideal points. We then provide numerous explicit examples, including certain two-bridge knots, 3-strand pretzel knots, and knots with non-integral toroidal surgeries. We also prove that the union of a once- and a twice-punctured torus inside the (-3, 5, 5) or (3, -5, -5) pretzel knot, both essential, is detected by an ideal point of the character variety and explicitly determine its limiting character.